Long Josephson Junctions (LJJs), so named because of a long length of the junction relative to the Josephson screening length, can support nonlinear solutions such as a flux soliton. A flux soliton, referred to sometimes with the more general term fluxon, is a soliton having total flux equal to Φ0, where Φ0 is the magnetic flux quantum. The shape of the soliton, and other excitations such as chains of fluxons and waves, follows from the Sine-Gordon equation describing the junction. These solitons have been found in practice to dissipate energy as they move, and near the maximum velocity they can create waves at short wavelengths, known as Cherenkov radiation. An LJJ with a soliton drive current has been used to read out a superconducting qubit.
Flux solitons have been measured in an LJJ using superconducting classical logic, where a continuous LJJ makes direct contact to a powered Josephson transmission line (PJTL). Logic families such as Rapid Single Flux Quantum and Reciprocal Quantum Logic have the PJTLs and other powered junctions to propagate fluxons and create gates, respectively. However, the Josephson Junctions in these structures switch individually due to the supplied power and the presence of “localized,” or “discrete” fluxons residing within one unit cell of a JTL. These logic families are irreversible, and switch due to an energy, orders of magnitude greater than the theoretical limit defined by kB*T*ln(2) (where kB is the Boltzmann constant), that is supplied by the power source for the switching event.
It has long been recognized that kB*T*ln(2) defines a theoretical floor for the amount of energy that is dissipated by a computation that creates one bit of physical entropy, known as the Neumann-Landauer limit, and that conventional computer processing dissipates heat exceeding this amount by orders of magnitude. It similarly has been theorized that this limit would not come into play for computational processes that are both logically and physically reversible, because fully reversible processes do not increase total entropy. However, computational gates and circuits approaching such theoretically possible levels of efficiency have not been demonstrated in previous systems. Note that quantum bits in quantum information research are reversible by themselves, but their control systems have not been designed for efficiency, such that logic operations in these systems also dissipate energy much greater than kB*T*ln(2) per operation.